Coherent beam combination (CBC) of laser amplifiers is a well-established technique for locking multiple laser emitters in phase with one another to form a high brightness beam. Typically, the output from a low-power master oscillator (MO) is split into a multiplicity of beams, each of which is passed through a laser amplifier to increase its power. The amplified output beams are combined geometrically and phase-locked to a reference beam that is also derived from the MO. The combined beam behaves as if it were emitted from a single aperture laser, but with higher brightness than can be obtained from an individual laser. CBC imposes a requirement that the optical path length through each laser amplifier in the phase-locked array must be matched to within a small fraction of the MO coherence length. If the optical path mismatch between any two elements exceeds the coherence length, then the two elements will appear to be incoherent with one another, and they cannot be successfully phase-locked. Even if the optical path mismatch is only a fraction of the coherence length, the coherence between the two lasers will be less than 100%, leading to a reduction in the array brightness.
Due to the long path lengths involved with either free-space or fiber amplifiers (typically >10 m), it is difficult to match paths to within less than a few cm. Different amounts of thermal expansion or strain in each amplifier can cause the path mismatches to vary dynamically with the laser environment or thermal loads. This typically leads to a requirement that the MO coherence length be much greater than the anticipated path mismatches. The coherence length scales inversely with the laser bandwidth according toLcoh=cτcoh≈c/Δf,  (1)where c is the speed of light, and Δf is the laser bandwidth. Thus a practical path-matching tolerance of ˜10 cm leads to a requirement that the laser bandwidth be several GHz or less.
In practice, the constraint is more restrictive than this to avoid any noticeable reduction in the coherence between individual emitters. For the case of fiber laser amplifiers, the use of narrow-band radiation from the MO imposes limits on the capacity to generate high power. Stimulated Brillouin Scattering (SBS) is a nonlinear effect in which the laser electric field creates a phase grating in the fiber core via electrostriction that reflects some fraction of the forward-propagating beam. If the effective reflectivity of this grating becomes too large, the output power from the fiber will decrease, with the lost power being reflected backwards towards the MO. SBS limits the powers available from narrow-bandwidth fiber lasers. SBS can also pose a damage risk to hardware if the reflected power feeds back into the MO and/or pre-amplifier. One approach to CBC requires a means to reduce SBS. Typically, this involves a controlled broadening of the MO spectrum, either via a rapidly varying chirp applied to the MO frequency or via static phase modulation. In either case, practical considerations of the path-matching stability between amplifier legs limits the amount of frequency broadening to several GHz.